Best Known (28−8, 28, s)-Nets in Base 16
(28−8, 28, 1542)-Net over F16 — Constructive and digital
Digital (20, 28, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 4, 514)-net over F16, using
- s-reduction based on digital (2, 4, 4369)-net over F16, using
- digital (4, 8, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 4, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 4, 257)-net over F256, using
- digital (8, 16, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
- digital (2, 4, 514)-net over F16, using
(28−8, 28, 8192)-Net in Base 16 — Constructive
(20, 28, 8192)-net in base 16, using
- net defined by OOA [i] based on OOA(1628, 8192, S16, 8, 8), using
- OA 4-folding and stacking [i] based on OA(1628, 32768, S16, 8), using
- discarding factors based on OA(1628, 32771, S16, 8), using
- discarding parts of the base [i] based on linear OA(3222, 32771, F32, 8) (dual of [32771, 32749, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3219, 32768, F32, 7) (dual of [32768, 32749, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding parts of the base [i] based on linear OA(3222, 32771, F32, 8) (dual of [32771, 32749, 9]-code), using
- discarding factors based on OA(1628, 32771, S16, 8), using
- OA 4-folding and stacking [i] based on OA(1628, 32768, S16, 8), using
(28−8, 28, 14771)-Net over F16 — Digital
Digital (20, 28, 14771)-net over F16, using
(28−8, 28, large)-Net in Base 16 — Upper bound on s
There is no (20, 28, large)-net in base 16, because
- 6 times m-reduction [i] would yield (20, 22, large)-net in base 16, but